Date of Award

8-2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

Committee Chair/Advisor

Yoon, Jeong-Rock

Committee Member

Brannan , James

Committee Member

Ervin , Vincent

Committee Member

Khan , Taufiquar

Abstract

This thesis is for a sensitivity analysis of magnetic resonance elastography, a hybrid imaging technique used in early-stage cancer screening. To quantitatively analyze the sensitivity, we introduce a notion of detectability, which is dened as a relative amplitude
drop in a small sti tumor region. This analysis is accomplished in both the full elastic and viscoelastic models and compared with that of the simpler scalar model which is frequently used in the actual application.
Some of the highlights are 1) a useful formula for detectability in terms of physical parameters, which will help the design of experiments; 2) the discrepancy between the full elastic model and the scalar model that provides a criterion when the simple scalar model is acceptable; 3) a theoretical limit of the smallest tumor that magnetic resonance elastography can reconstruct; 4) the existence of optimal frequency when the Voigt (viscoelastic) model is
adopted; and 5) the limit behavior of the solution when the inclusion stiness or attenuation becomes innitely high.
We expect that this detectability approach is extendable to many hybrid imaging techniques to quantify their sensitivities and cross-compare them to determine which modality is the most powerful in detecting early-stage cancer.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.